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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is
  • ✓
    $[t^{-1} u^{-2}\,I^{1}]$
  • B
    $[t^{1} u^{2}\,I^{-1}]$
  • C
    $[t^{-2} u^{-1}\,I^{1}]$
  • D
    $[t^{-1} u^{1}\,I^{-2}]$
✓

Answer

Correct option: A.
$[t^{-1} u^{-2}\,I^{1}]$
a
$m \propto t^{a} v^{b} \ell^{c}$

$m \propto[T]^{a}\left[L T^{-1}\right]^{b}\left[M L^{2} T^{-1}\right]^{c}$

$M^{1} L^{0} T^{0}=M^{c} L^{b+2 c} T^{a-b-c}$

comparing powers

$v=1, b=-2, a=-1$

$m \propto t^{-1} v^{-2} \ell^{1}$

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